Problem 5
In triangle ABC, points M and N lie on AB and AC, respectively, and MB=BC=CN. If R and r are the circumradius and inradius of ABC, express MN/BC in terms of R and r.
Step 2 of 5: Find the second perpendicular
Detailed analysis
Because MB=BC, triangle MBC is isosceles and BI, which bisects angle ABC, is its perpendicular bisector of MC. Since I and D lie on BI, ID is perpendicular to MC.